X-ray reflectometry (XRR) is a well-known technique for measuring the thickness, density and surface quality of thin film layers deposited on a substrate. Such reflectometers typically operate by irradiating a sample with a beam of X-rays at grazing incidence, i.e., at a small angle relative to the surface of the sample, in the vicinity of the total external reflection angle of the sample material. Measurement of the X-ray intensity reflected from the sample as a function of angle gives a pattern of interference fringes, which is analyzed to determine the properties of the film layers responsible for creating the fringe pattern. The X-ray intensity measurements are commonly made using a position-sensitive detector.
Various types of position-sensitive X-ray detectors are known in the art of reflectometry. Solid-state arrays typically comprise multiple detector elements, which are read out by a charge-coupled device (CCD) or other scanning mechanism. The signals at low angles, below the total external reflection angle, are usually much stronger than the signals above this angle, although in both cases there may be random, relatively large signal excursions.
In order to obtain accurate measurements of reflected beams, it is necessary to precisely calibrate the angular scale of the reflection. Such a calibration requires, inter alia, exact control of the zero angle of reflection, so that the angle of the reflected beam relative to the surface can be determined accurately. (In the context of the present patent application and in the claims, the term “zero angle” refers to the orientation of a tangent to the reflecting surface at the point of incidence of the radiation.) To make reflectometric measurements with optimal accuracy, the zero angle at the measurement point should be known to within 0.001°.
Although semiconductor wafers appear to be flat, in practice wafers typically deform slightly when held by a vacuum chuck during production or inspection. The deformation is due both to the vacuum force exerted by the chuck and to the weight of the wafer itself. Furthermore, the chuck may have imperfections, such as a slight bend in its axis, that cause deviations in the zero angle of the wafer as it rotates. As a result, inclination of the surface at different sample points on the surface of a wafer may vary by as much as 0.1–0.2°. Therefore, to perform accurate reflectometric measurements at a well-defined measurement point, it becomes necessary to recalibrate the zero angle at each point that is tested on the wafer surface.
In an X-ray reflectometer, the irradiating X-ray beam is typically filtered in a monochromator, and is also focused onto a small region of the surface being analyzed. A number of systems which act both as a monochromator and as a focusing element are known in the art. Such combined systems typically use curved crystals, the operation of which is based on the Bragg X-ray reflection law:nλ=2d sin(θB)  (1)
where n is a diffractive order of X-rays of wavelength λ diffracted from crystal planes having a spacing d, and θB is the angle between an incident X-ray beam and the crystal planes.
U.S. Pat. No. 5,923,720, to Barton et al., whose disclosure is incorporated herein by reference, describes an X-ray spectrometer based on a curved crystal monochromator. The monochromator has the shape of a tapered logarithmic spiral, which is described as achieving a finer focal spot on a sample surface than prior art monochromators, a number of which are also described in the disclosure.
U.S. Pat. No. 6,711,232, to Janik, whose disclosure is incorporated herein by reference, describes X-ray measurements using a linear X-ray source having an axis at right angles to the surface of a sample being measured. A beam from the source is focused by a reflector onto the sample. Alternative arrangements describe two linear sources with axes at right angles to the sample surface. The two sources generate respective X-ray beams which are focused by two reflectors onto the sample.
XOS Inc., of Albany, N.Y., produce the Doubly-Bent Focusing Crystal Optic, which comprises a single crystal having two orthogonal radii of curvatures. The two radii of curvatures enable the crystal to act both as a focusing element and as a monochromator. Crystals having two radii of curvatures in different directions, such as those exemplified by the Doubly-Bent Focusing Crystal Optic, are herein termed doubly-curved crystals (DCCs) or DCC optics. DCC optics are formed from crystals such as mica, quartz, or silicon.
DCC optics typically incorporate an idea first suggested in 1882 by Rowland for optical gratings. Rowland demonstrated that a grating ruled on a spherical mirror having a radius 2R would focus all orders of spectra from the mirror onto a circle of radius R if the source of radiation irradiating the curved grating is also on the circle. The circle is termed the Rowland circle. The X-ray source, the DCC optic, and the focused image of the X-ray source all lie on the Rowland circle.